Calcul stalpi beton armat

8/10/2019 Calcul stalpi beton armat

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Calculul raportului Mrb/Medb pentru tronsonul 2 de stlp, E1

Seism ST-DR

MRb 3 156.4 kN m 3 269.5 kN m+ 1277.7 kN m=:= MEdb 110 218+ 110+ 214.5+ 123.3+ 222.5+( ) kN m 998.3kN m=:=

MRb MEdb

1.28=

Seism DR-ST

MRb 3 156.4 kN m 3 269.5 kN m+ 1277.7 kN m=:= MEdb 223.6 123.2+ 215.5+ 112+ 219.7+ 110.2+( ) kN m 1004.2kN m=:=

MRb MEdb

1.272=

3


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Calculul raportului Mrb/Medb pentru tronsonul de stlp E2 si E3

Seism ST-DR

MRb 3 108.2 kN m 3 182.3 kN m+ 871.5 kN m=:= MEdb 49.7 166.35+ 68.3+ 171.65+ 74.4+ 174.3+( ) kN m 704.7kN m=:=

MRb MEdb

1.237=

Seism DR-ST

MRb

3 108.2 kN m 3 182.3 kN m+ 871.5 kN m=:= MEdb 176.16 74.6+ 173.4+ 70.4+ 168.4+ 50.35+( ) kN m 713.31kN m=:=

MRb MEdb

1.222=

4


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Calculul ariilor de armtur longitudinal

Caracteristicile sectiunii c 1.2:= s 1:= combinatie seismich 500mm:= b 500mm:=

f ck 25 N

mm 2:= f cd 20.8

N

mm 2:= f ctm 2.6

N

mm 2:=Beton C25/30

f yd 345 N

mm 2:=O el PC52

Clasa de ductilitate medie M Rd 1.2:=

Acoperirea cu beton

max 20mm:= cmin max 20mm=:= cdev 10mm:=

cnom cmin cdev+ 30mm=:= ds cnomcmin

2+ 40mm=:=

d h ds 460mm=:= hs h 2 ds 420mm=:=

5


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Tronsonul 1- Parter -ST50x50

Momentele 1 si 4 provin din Seism ST-DRMomentele 2 si 3 provin din Seism DR-ST

MEd1 203.3kN m:= MEd2 203.6kN m:= NEd1 850kN:=

e0 20mm=MEd4 159.3kN m:= MEd3 160kN m:=

MEdc1 MEd1 NEd1 e0+( ) 225.673 kN m=:=Md1 Rd MEdc1 1.107 299.78kN m=:=

xmin 1.882 ds 75.28mm=:=x1 NEd1

0.8 b f cd 102.163mm=:=

Asc1Md1 NEd 0.5 h 0.4 x1( )

f yd 0.5 h ds( ) x1 xminif

Md1 NEd 0.5 h ds( )f yd 0.5 h ds( )

x1 xmin


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MEdc2 MEd2 NEd1 e0+( ) 225.98 kN m=:=

Md2 Rd MEdc2 1.106 299.92kN m=:=

xmin 1.882 ds 75.28mm=:=x1 NEd1

0.8 b f cd 102.163mm=:=

Asc2Md2 NEd1 0.5 h 0.4 x1( )


Md2 NEd1 0.5 h ds( )f yd 0.5 h ds( )

x1 xmin


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MEdc2 MEd2 NEd2 e0+( ) 177.035 kN m=:=

Md2 Rd MEdc2 1.27 269.8kN m=:=

xmin 1.882 ds 75.28mm=:=x2 N

Ed0.8 b f cd

132.572mm=:=

Asc2Md2 NEd2 0.5 h 0.4 x2( )


Md2 NEd2 0.5 h ds( )f yd 0.5 h ds( )

x2 xmin


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Tronsonul 3-Etaj 2 -ST50x50


MEd1 115.8kN m:= MEd2 106.85kN m:= NEd3 447.5kN:=

MEd4 132.607kN m:= MEd3 121.45kN m:= e0 20mm=


xmin 1.882 ds 75.28mm=:=x3 NEd3

0.8 b f cd 53.786mm=:=

Asc1Md1 NEd3 0.5 h 0.4 x3( )


Md1 NEd3 0.5 h ds( )f yd 0.5 h ds( )

x3 xmin


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MEdc2 MEd2 NEd3 e0+( ) 118.624 kN m=:=

Md2 Rd MEdc2 1.222 173.95kN m=:=

xmin 1.882 ds 75.28mm=:=x3 NEd3

0.8 b f cd 53.786mm=:=

Asc2Md2 NEd3 0.5 h 0.4 x3( )


Md2 NEd3 0.5 h ds( )f yd 0.5 h ds( )

x3 xmin


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Tronsonul 4-Etaj 3 -ST50x50


MEd1 61.34kN m:= MEd2 54.67kN m:= NEd4 230.7kN:=

MEd4 74.37kN m:= MEd3 74.3kN m:= e0 20mm=


xmin 1.882 ds 75.28mm=:=x4 NEd4

0.8 b f cd 27.728mm=:=

Asc1Md1 NEd4 0.5 h 0.4 x4( )


Md1 NEd4 0.5 h ds( )f yd 0.5 h ds( )

x4 xmin


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MEdc2 MEd2 NEd e0+( ) 78.601 kN m=:=

Md2 Rd MEdc2 1.222 115.26kN m=:=

xmin 1.882 d s 75.28mm=:=x4 N

Ed40.8 b f cd

27.728mm=:=

Asc2Md2 NEd4 0.5 h 0.4 x4( )


Md2 NEd4 0.5 h ds( )f yd 0.5 h ds( )

x4 xmin


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Armare efectiv

Conform prevederilor constructive pentru stlpi din P100-2006 pentruasigurarea ductilit ii locale, coecientul de armare longitudinal total va cel pu in 0,008 i cel mult 0,04.

min 0.008:= max 0.04:=

Asc.min min b h 2000mm2=:= Asc.max max b h 10000mm

2=:=

Deoarece aria maxim rezultat din calcul in toate tronsoanele este 1954 mm 2si reprezint aria de armtur dispus simetric pe ambele par i, rezult oarmtura efectiv 4 20+618 (As=2774mm 2) pentru tronsoanele 1,2 si o

armatura efectiva 10 18 (As=2540 mm 2) pentru tronsoanele 3,4

Arie de armtur efectiv TR 1,2- 4 20+618 PC52 Asc.tot1 2774mm2:=

Arie de armtur efectiv TR 3,4- 10 18 PC52 Asc.tot2 2540mm2:=

Asc.tot aria de armtur longitudinal total pe o directie dispusa simetric

Calculul momentelor capabile

Tronson 1-Parter

x1 102.163mm= NEd1 1110kN:= xmin 75.28mm= x1 xmin>

MRc1 NEd1 0.5 h 0.4 x1( ) Asc.tot1 f yd 0.5 h ds( )+ x1 xminif NEd1 Asc.tot1 f yd+( ) 0.5 h ds( ) x1 xmin


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Tronson 3-Etaj 2

x3 53.786mm= NEd3 524kN:= xmin 75.28mm= x3 xmin>




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Dimensionarea la for e tietoare

For a tietoare de proiectare Vdc se determin din echilibrul stlpului peecare nivel, cnd la extremita i se consider momentele capabile cecorespund formrii articula iilor plastice ce apar n grinzile sau stlpii conecta iin nod.

Mdc.i Rd MRc.i MRb MRc

:= MRc.i Rd 1.0:= clas ductilitate M

MRc.i valoarea de proiectare a momentului capabil la extremitatea icorespunztoare sensului seismului

MRb valoarea momentelor capabile de la capetele grinzilor

MRc valoarea momentelor capabile de la capetele stlpilor, stabilite pe baza

valorilor for elor axiale din situa ia corespunztoare sensului consideratal ac iunii seismice

VdcMdc1 Mdc2+

lcl:=

Mdc1

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Condi ii pentru armtura transversal la stlpi ncadra i in clasa M

Distan a dintre etrieri

175mm 8 16 mmsw min dintre 520

2

sw.max 128mm:=

coecient de armare transversal n zona critic a stlpilor de la bazarespectiv restul zonelor critice de la celelalte niveluri

w.min1 0.0035:= w.min2 0.0025:=

Tronsonul 1-Parter

lcl 3.1m:= 1 nod inferior, 2 nod superior

MRb1 0:=

MRc1 MRc1 433.12kN m=:=

MRb2 269.5 154.4+( ) kN m 423.9kN m=:=

MRc2 MRc1 MRc2+ 819.989 kN m=:=

Mdc1 Rd MRc1 1 433.12kN m=:=

Mdc2 Rd MRc1 MRb2 MRc2

223.903 kN m=:=

Vdc1Mdc1 Mdc2+

lcl211.941kN=:=

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Dimensionarea armturii transversale

CRd.c0.18

c

0.15=:= k 1 200mmd

+ 1.66=:= k 2< condi ie ndeplinit

Asl 2512mm2:= l

Asl

b d 0.0109=:= l 0.02< condi ie ndeplinit

cp1103 10 3

500 500 4.412=:= k 1 0.15:=

VRd.c CRd.c k k 1 cp 100 l f ck mm2

N+

1

3

b d N

mm 2 173.77kN=:=

VRd.c.min 0.035 k 1.5 f ck

mm 2

N

0.5 b d

N

mm 2 86.037kN=:=

VRd.c VRd.c.min>

Dimensionarea armturii transversale din zona critic

VEd Vdc1 211.94kN=:= VEd VRd.c> z 0.9 d 414mm=:=

Se calculeaza etrierii necesariAsw - aria sectiuniiarmaturii transversaleAsw

sw

.necVEd

z f ywd:= Sef

Asw.ef

Asw

sw

.nec

:=Sw - distan a ntre etrieri

etrieri o el PC52 f ywd 345 N

mm 2:=

Se impune 8mm:= - diamentrul etrierilor

n brate 4:= A1.etr 50.3mm2

:=Asw n brate A1.etr 201.2 mm

2=:= Sef Asw z f ywd( )

VEd135.591 mm=:=

Se alege 8 /10cm 80mm < S ef < 128mm, M50 => sw 100mm:=

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Armtur transversal format din 2 etrieri (4 bra e) 8/10 PC52

w w.min>w

Asw

b sw 0.00402=:=

Tronsonul 2-Etaj 1


MRb1 269.5 154.4+( ) kN m 423.9kN m=:=

MRc1 MRc1 MRc2+ 819.99 kN m=:=

MRb2 269.5 154.4+( ) kN m 423.9kN m=:=

MRc2 MRc2 MRc3+ 680.936 kN m=:=


200kN m=:=


240.84 kN m=:=

Vdc2Mdc1 Mdc2+

lcl169.552kN=:=

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CRd.c0.18

c0.15=:= k 1

200mm

d+ 1.66=:= k 2< condi ie ndeplinit

Asl 2412mm2:= l

Asl


cp810 10 3

500 500 3.24=:= k 1 0.15:=

VRd.c

CRd.c

k k 1

cp

100 l f

ck

mm2

N+

1

3

b d N

mm 2 171.115kN=:=


mm 2

N

0.5

b d N

mm 2 86.037kN=:=

VRd.c VRd.c.min> VRd.c Vdc1> armare din condi ii constructive


sw 120mm:= Asw.min w.min2 b sw 150mm2

=:=


n brate 4:= A1.etr 50.3mm2:=

Asw n brate A1.etr 201.2 mm2=:=


w 0.0025>wAsw b sw

0.0034=:=

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Tronsonul 3-Etaj 2


MRb1 269.5 154.4+( ) kN m 423.9kN m=:=


MRb2 182.3 108.2+( ) kN m 290.5kN m=:=

MRc2 MRc3 MRc4+ 531.342 kN m=:=


183.06 kN m=:=


160.77 kN m=:=

Vdc3Mdc1 Mdc2+

lcl132.244kN=:=

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CRd.c0.18

c0.15=:= k 1 200mm


Asl 2412mm2:= l

Asl


cp520 10 3

500 500 2.08=:= k 1 0.15:=


N+

1

3 b d

N

mm 2 170.742kN=:=


mm 2

N

0.5

b d N

mm 2 86.037kN=:=



sw 120mm:= Asw.min w.min2 b sw 150mm2=:=





w 0.0025>wAsw

b sw 0.0034=:=

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Tronsonul 4-Etaj 3


MRb1 182.3 108.2+( ) kN m 290.5kN m=:=


MRb2 182.3 108.2+( ) kN m 290.5kN m=:=

MRc2 MRc4 237.279kN m=:=


129.73 kN m=:=

Mdc2 Rd MRc4 1 237.28kN m=:=

Vdc3Mdc1 Mdc2+

lcl

141.156kN=:=

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Calculul raportului Mrb/Medb pentru tronsonul 1 de stlp, P

Seism ST-DR

MRb 3 156.4 kN m 3 269.5 kN m+ 1277.7 kN m=:= MEdb 149 250+ 126.9+ 231.5+ 146.58+ 250.5+( ) kN m 1154.48kN m=:=

MRb MEdb

1.107=

Seism DR-ST


MRb MEdb

1.106=

26


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Calculul raportului Mrb/Medb pentru tronsonul 2 de stlp, E1

Seism ST-DR

MRb 3 156.4 kN m 3 269.5 kN m+ 1277.7 kN m=:= MEdb 110 218+ 110+ 214.5+ 123.3+ 222.5+( ) kN m 998.3kN m=:=

MRb MEdb

1.28=

Seism DR-ST

MRb 3 156.4 kN m 3 269.5 kN m+ 1277.7 kN m=:= MEdb 223.6 123.2+ 215.5+ 112+ 219.7+ 110.2+( ) kN m 1004.2kN m=:=

MRb MEdb

1.272=

27


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Calculul raportului Mrb/Medb pentru tronsonul 3 de stlp E2

Seism ST-DR


MRb MEdb

1.237=

Seism DR-ST

MRb 3 108.2 kN m 3 182.3 kN m+ 871.5 kN m=:= MEdb 176.16 74.6+ 173.4+ 70.4+ 168.4+ 50.35+( ) kN m 713.31kN m=:= MRb MEdb

1.222=

28


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Calculul ariilor de armtur longitudinal

Caracteristicile sectiunii c 1.2:= s 1:= combinatie seismich 500mm:= b 500mm:=

f ck 25 Nmm 2

:= f cd 20.8 Nmm 2

:= f ctm 2.6 Nmm 2

:=Beton C25/30

f yd 345 N

mm 2:=O el PC52

Clasa de ductilitate medie M Rd 1.2:=

Acoperirea cu beton

max 20mm:= cmin max 20mm=:= cdev 10mm:=

cnom cmin cdev+ 30mm=:= ds cnomcmin

2+ 40mm=:=

d h ds 460mm=:= hs h 2 ds 420mm=:=

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Tronsonul 1- Parter -ST50x50


MEd1 193kN m:= MEd2 170kN m:= NEd1 345kN:=e0 20mm=MEd4 90.35kN m:= MEd3 138.7kN m:=


xmin 1.882 ds 75.28mm=:=x1 NEd1

0.8 b f cd

41.466mm=:=

Asc1Md1 NEd 0.5 h 0.4 x1( )


Md1 NEd 0.5 h ds( )f yd 0.5 h ds( )

x1 xmin


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MEdc2 MEd2 NEd1 e0+( ) 181.215 kN m=:=

Md2 Rd MEdc2 1.106 240.51kN m=:=

xmin 1.882 ds 75.28mm=:=x1 NEd1

0.8 b f cd 41.466mm=:=

Asc2Md2 NEd1 0.5 h 0.4 x1( )


Md2 NEd1 0.5 h ds( )f yd 0.5 h ds( )

x1 xmin


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Asc4Md4 NEd1 0.5 h 0.4 x1( )


Md4 NEd1 0.5 h ds( )f yd 0.5 h ds( )

x1 xmin


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Asc1Md1 NEd2 0.5 h 0.4 x2( )


Md1 NEd2 0.5 h ds( )f yd 0.5 h ds( )

x2 xmin


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xmin 1.882 ds 75.28mm=:=x3 NEd3

0.8 b f cd 25.3mm=:=

Asc1

Md1 NEd3 0.5 h 0.4 x3( )f yd 0.5 h ds( ) x3 xminif

Md1 NEd3 0.5 h ds( )f yd 0.5 h ds( )

x3 xmin


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Md4 Rd MEdc4 1.237 185.22kN m=:=

xmin 1.882 d s 75.28mm=:=x3 NEd3

0.8 b f cd 25.3mm=:=

Asc4Md4 NEd3 0.5 h 0.4 x3( )


Md4 NEd3 0.5 h ds( )f yd 0.5 h ds( )

x3 xmin


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Tronson 2-Etaj 1

x2 34.075mm= NEd2 512kN:= xmin 75.28mm=

MRc2

NEd2

0.5 h 0.4 x2

( )

Asc.tot1

f yd

0.5 h ds

( )

+ x2

xmin

if

NEd2 Asc.tot1 f yd+( ) 0.5 h ds( ) x2 xmin




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Dimensionarea la for e tietoare

For a tietoare de proiectare Vdc se determin din echilibrul stlpului peecare nivel, cnd la extremita i se consider momentele capabile cecorespund formrii articula iilor plastice ce apar n grinzile sau stlpii conecta iin nod.

Mdc.i Rd MRc.i MRb MRc

:= MRc.i Rd 1.0:= clas ductilitate M

M valoarea de proiectare a momentului capabil la extremitatea i40


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. corespunztoare sensului seismului

MRb valoarea momentelor capabile de la capetele grinzilor

MRc valoarea momentelor capabile de la capetele stlpilor, stabilite pe bazavalorilor for elor axiale din situa ia corespunztoare sensului considerat

al ac iunii seismice

VdcMdc1 Mdc2+

lcl:=

Mdc1

Condi ii pentru armtura transversal la stlpi ncadra i in clasa M

Distan a dintre etrieri175mm 8 16 mmsw min dintre

520

2

sw.max 128mm:=

coecient de armare transversal n zona critic a stlpilor de la bazarespectiv restul zonelor critice de la celelalte niveluri

w.min1 0.0035:= w.min2 0.0025:=

Tronsonul 1-Parter


MRb1 0:=

MRc1 MRc1 359.63kN m=:=

MRb2 269.5 154.4+( ) kN m 423.9kN m=:=


Mdc1 Rd MRc1 1 359.63kN m=:=


225.094 kN m=:=

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Vdc1Mdc1 Mdc2+

lcl188.619kN=:=


CRd.c 0.18 c0.15=:= k 1 200mm


Asl 2512mm2:= l

Asl


cp712 10 3

500 500 2.848=:= k 1 0.15:=


N+

1

3

b d N

mm 2 173.283kN=:=


mm 2

N

0.5

b d N

mm 2 86.037kN=:=

VRd.c VRd.c.min>

Dimensionarea armturii transversale din zona critic

VEd Vdc1 188.62kN=:= VEd VRd.c> z 0.9 d 414mm=:=

Se calculeaza etrierii necesariAsw - aria sectiuniiarmaturii transversaleAsw

sw

.nec

VEd

z f ywd:= Sef

Asw.ef

Asw

sw

.nec

:=Sw - distan a ntre etrieri

etrieri o el PC52 f ywd 345 N

mm 2:=



42


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Asw n brate A1.etr 201.2 mm2=:= Sef

Asw z f ywd( )VEd

152.357 mm=:=

Se alege 8 /10cm 80mm < S ef < 128mm, M50 => sw 100mm:=


w w.min>wAsw

b sw 0.00402=:=

Tronsonul 2-Etaj 1


MRb1 269.5 154.4+( ) kN m 423.9kN m=:=


MRb2 269.5 154.4+( ) kN m 423.9kN m=:=

MRc2 MRc2 MRc3+ 569.268 kN m=:=


198.81 kN m=:=


236.52 kN m=:=

Vdc2

Mdc1 Mdc2+

lcl167.432kN=:=


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CRd.c0.18

c0.15=:= k 1 200mm


Asl 2512mm2:= l

Asl


cp512 10 3500 500

2.048=:= k 1 0.15:=


N+

1

3

b d N

mm 2 173.033kN=:=


mm 2

N

0.5

b d N

mm 2 86.037kN=:=





n brate 4:= A1.etr 50.3mm2

:=



w 0.0025>wAsw

b sw 0.0034=:=

Tronsonul 3-Etaj 2lcl 2.6m:= 1 nod inferior, 2 nod superior

MRb1 269.5 154.4+( ) kN m 423.9kN m=:=


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MRb2 182.3 108.2+( ) kN m 290.5kN m=:=

MRc2 MRc3 MRc4+ 466.536 kN m=:=


187.38 kN m=:=


156.69 kN m=:=

Vdc3Mdc1 Mdc2+

lcl132.337kN=:=


CRd.c0.18

c0.15=:= k 1 200mm


Asl 2512mm2

:= lAsl


cp322 10 3

500 500 1.288=:= k 1 0.15:=


N+

1

3

b d N

mm 2 172.794kN=:=

VRd.c.min

0.035 k 1.5 f ck

mm 2

N

0.5

b d N

mm 2 86.037kN=:=



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n brate

4:= A1.etr

50.3mm 2:=



w 0.0025>wAsw

b sw 0.0034=:=

Tronsonul 4-Etaj 3


MRb1 182.3 108.2+( ) kN m 290.5kN m=:=


MRb2 182.3 108.2+( ) kN m 290.5kN m=:=

MRc2 MRc4 214.893kN m=:=


133.81 kN m=:=

Mdc2 Rd MRc4 1 214.89kN m=:=

Vdc3Mdc1 Mdc2+

lcl134.116kN=:=

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CRd.c0.18

c0.15=:= k 1 200mm


Asl 2512mm2:= l

Asl b d

0.0109=:= l 0.02< condi ie ndeplinit

cp230 10 3

500 500 0.92=:= k 1 0.15:=


N+

1

3

b d N

mm 2 172.679kN=:=

VRd.c.min 0.035 k 1.5 f ck mm 2

N

0.5

b d N

mm 2 86.037kN=:=








w w.min2>wAsw

b sw 0.0034=:=

Documents

Calcul stalpi beton armat